mcll (version 1.2)

mcll_est: Parameter estimation using MCLL

Description

Parameter estimation using Monte Carlo local likelihood

Usage

mcll_est(data, prior.func, alp=0.7, method="BFGS",  lower = -Inf, upper = Inf, control=list(), use.locfit=TRUE, con.manual=list(method="BFGS", lower = -Inf, upper = Inf, control=list()) )

Arguments

data

posterior samples of model parameters. a matrix or data.frame of size $m \times p$ ($m$: sample size, $p$: dimension of the parameters).

prior.func

a prior function. An argument should be a vector of parameter values and a return value should be the log prior density for those parameter values.

alp

a real value between 0 and 1. $\alpha$ takes a value between 0 and 1, which is the nearest neighbor bandwidth with the $k$th smallest distance $d$ where $k = \lfloor n \alpha \rfloor$ and $d(x, x_{i}) = | x - x_{i} | $ with the sample size $n$

method

an optimization method to be used in maximizing the approximation to the unnormalized log-likelihood. Options from optim are Nelder-Mead, BFGS, CG, L-BFGS-B, and SANN.

lower, upper

bounds on the variables for the L-BFGS-B method in optim.

control

a list of control parameters. See control options for optim.

use.locfit

logical. If TRUE, locfit is used to compute a local likelihood density estimate. If FALSE, a code from the mcll package is used. locfit is typically faster but sometimes fails for high-dimensional parameter spaces.

con.manual

a list. An optimization method for finding the polynomial coefficients, lower and upper bounds on the variables for the L-BFGS-B method, and a list of control parameters when use.locfit = FALSE. See control options for optim.

Value

mcll_est returns a list of the following components,

par

parameter estimates on the original scale.

value

value of the function corresponding to par. This is an unnormalized log-likelihood from the MCLL algorithm. One can use this to compute the Bayes factor. For details, see Appendix of Jeon et al. (2012).

counts

a two-element integer vector giving the number of calls to function and gradient, respectively.

convergence

an integer code. 0 indicates successful completion. For possible error codes, see the document for optim.

message

a character string giving any additional information returned by optim, or NULL.

Details

Nested maximizations in Step 2 in the Monte Carlo local likelihood estimation. It makes use of the R package locfit and the R function optim. The posterior samples should be on the real line (e.g., variance parameters should be on the log-scale). The prior distributions (provided as a form of prior.func) should be the same as those used for obtaining the posterior samples of the model parameters. For details, see Section 2 in Jeon et al. (2012).

References

Jeon, M., Kaufman, C., and Rabe-Hesketh, S. (2014). Monte Carlo local likelihood for approximate MLE of complex models. Under revision.

Loader, C. (2012). locfit: Local regression, likelihood, and density estimation. Downloadable from http://cran.r-project.org/web/packages/locfit/index.html.

See Also

mcll_se

Examples

## example

# posterior samples
data(samp)

# prior function
prior.func <- function(vec.t) {
    sum(dnorm(vec.t, m= c(0,0,0,0, -0.9870405, -0.9870405) ,
                sd=c(100,100,100,100, 1/0.766672, 1/0.766672) , log=TRUE))
}

## parameter estimation
run1 <- system.time(
    result1 <- mcll_est(data=samp, prior.func= prior.func, alp=0.7,
        method = "BFGS", control= list(maxit=10000))
)

# result1$par
#            b0        b1         b2       b3       tau0     tau1
#[1,] 0.9275766 -2.871686 -0.6488625 3.589313 0.08118962 0.148478